Details

analyze1.4s (4.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample12.1s (39%)

Results

3.9s	4024×	body	1024	valid
3.4s	3957×	body	1024	invalid
1.5s	2031×	body	512	valid
1.3s	2119×	body	512	invalid
914.0ms	502×	body	2048	valid
455.0ms	993×	body	256	invalid
438.0ms	992×	body	256	valid
180.0ms	707×	body	128	valid
3.0ms	3×	body	2048	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 116 to 92 computations (20.7% saved)

simplify48.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-neg_binary64`
569×	`fma-def_binary64`
365×	`div-sub_binary64`
240×	`associate-/r*_binary64`
202×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	295	55
4	736	55
5	1625	55
6	4003	55
7	5053	55

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

60.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.8b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))

Status

Error

Program

▶

60.8b

(neg.f64 (*.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))

Compiler

Compiled 146 to 112 computations (23.3% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))))
✓	0.3b	(*.f64 (/.f64 (PI.f64) 4) f)
✓	0.8b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))))
✓	5.3b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))

series738.0ms (2.4%)

Counts

4 → 48

Calls

4 calls:

685.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))))
42.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))))
7.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))
3.0ms	(*.f64 (/.f64 (PI.f64) 4) f)

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary64`
74×	`add-sqr-sqrt_binary64`
70×	`times-frac_binary64`
45×	`add-cube-cbrt_binary64`
36×	`log-prod_binary64`

Counts

4 → 173

Calls

4 calls:

8.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
8.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))))
7.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))))
4.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))

simplify357.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-def_binary64`
386×	`fma-neg_binary64`
279×	`times-frac_binary64`
217×	`cancel-sign-sub-inv_binary64`
191×	`exp-prod_binary64`

Counts

221 → 294

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	342	11438
1	753	10366
2	2176	10137
3	4369	10122
4	4977	10122
5	4874	10122

prune523.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	463	5	468
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	464	5	469

Error

1.6b

Counts

469 → 5

Alt Table

Status	Error	Program
	3.1b	(neg.f64 (*.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f))))
	1.9b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (+.f64 (log.f64 1/2) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))))
▶	1.8b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f)))))))
	60.8b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (sqrt.f64 (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))))) (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (sqrt.f64 (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))))
	2.7b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))

Compiler

Compiled 23308 to 17565 computations (24.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))
✓	1.1b	(log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (.f64 (/.f64 (PI.f64) 4) f)))))
✓	1.1b	(.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (.f64 (/.f64 (PI.f64) 4) f))))
✓	1.2b	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f)))

series1.6s (5%)

Counts

4 → 48

Calls

4 calls:

719.0ms	(log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (.f64 (/.f64 (PI.f64) 4) f)))))
716.0ms	(.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))
67.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f)))
59.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (.f64 (/.f64 (PI.f64) 4) f))))

rewrite109.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
131×	`add-sqr-sqrt_binary64`
109×	`*-un-lft-identity_binary64`
87×	`add-cube-cbrt_binary64`
72×	`associate-l_binary64`

Counts

4 → 238

Calls

4 calls:

24.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (.f64 (/.f64 (PI.f64) 4) f))))
22.0ms	(.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))
11.0ms	(log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (.f64 (/.f64 (PI.f64) 4) f)))))
6.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (*.f64 (/.f64 (PI.f64) 4) f)))

simplify374.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-def_binary64`
294×	`associate-r_binary64`
267×	`associate-l_binary64`
261×	`*-commutative_binary64`
240×	`associate-*l/_binary64`

Counts

286 → 404

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	434	14366
1	1095	13599
2	3894	13588
3	4888	13588
4	4940	13588

prune897.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	395	9	404
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	399	10	409

Error

1.3b

Counts

409 → 10

Alt Table

Status	Error	Program
	1.8b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (/.f64 (PI.f64) 4))) (.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (/.f64 4 (PI.f64))))))
	2.9b	(neg.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 (/.f64 (PI.f64) 4))) (log.f64 (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (.f64 (/.f64 (PI.f64) 4) f)))))))))
	1.8b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (log.f64 (.f64 2 (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
	2.5b	(neg.f64 (-.f64 (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))) (+.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))))))
	2.0b	(neg.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))) 3)))
▶	1.8b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
	2.7b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))
	2.0b	(neg.f64 (.f64 (.f64 (sqrt.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 (/.f64 4 (PI.f64)))) (.f64 (sqrt.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 (/.f64 4 (PI.f64))))))
	1.8b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (/.f64 (sqrt.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))))))
	2.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (cbrt.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))))) (cbrt.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))))))

Compiler

Compiled 24229 to 18716 computations (22.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))
✓	0.7b	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))
✓	1.2b	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))
✓	1.7b	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))

series2.1s (6.9%)

Counts

4 → 48

Calls

4 calls:

855.0ms	(.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))
794.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))
433.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))
63.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))

rewrite69.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`times-frac_binary64`
121×	`*-un-lft-identity_binary64`
115×	`log-prod_binary64`
94×	`add-sqr-sqrt_binary64`
89×	`add-cube-cbrt_binary64`

Counts

4 → 228

Calls

4 calls:

13.0ms	(.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))
7.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))
7.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))
6.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))

simplify364.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1012×	`times-frac_binary64`
239×	`associate-r_binary64`
227×	`*-commutative_binary64`
216×	`associate-/l*_binary64`
215×	`fma-def_binary64`

Counts

276 → 299

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	540	17828
1	1342	16830
2	4299	16825
3	6217	16825

prune688.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	299	0	299
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	299	10	309

Error

1.3b

Counts

309 → 10

Alt Table

Status	Error	Program
▶	1.8b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (/.f64 (PI.f64) 4))) (.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (/.f64 4 (PI.f64))))))
	2.9b	(neg.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 (/.f64 (PI.f64) 4))) (log.f64 (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (.f64 (/.f64 (PI.f64) 4) f)))))))))
	1.8b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (log.f64 (.f64 2 (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
	2.5b	(neg.f64 (-.f64 (+.f64 (.f64 1/12 (.f64 (pow.f64 f 2) (PI.f64))) (.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))) (+.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3))))))
	2.0b	(neg.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))) 3)))
✓	1.8b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
	2.7b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))
	2.0b	(neg.f64 (.f64 (.f64 (sqrt.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 (/.f64 4 (PI.f64)))) (.f64 (sqrt.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 (/.f64 4 (PI.f64))))))
	1.8b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (/.f64 (sqrt.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))))))
	2.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (cbrt.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))))) (cbrt.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))))))

Compiler

Compiled 22002 to 16982 computations (22.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (/.f64 4 (PI.f64))))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 (/.f64 (PI.f64) 4))) (.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (/.f64 4 (PI.f64)))))
✓	0.3b	(*.f64 f (/.f64 (PI.f64) 4))
✓	1.0b	(/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))

series1.6s (5.1%)

Counts

4 → 48

Calls

4 calls:

783.0ms	(.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (/.f64 4 (PI.f64))))
739.0ms	(.f64 (sqrt.f64 (/.f64 1 (/.f64 (PI.f64) 4))) (.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (/.f64 4 (PI.f64)))))
64.0ms	(/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))
3.0ms	(*.f64 f (/.f64 (PI.f64) 4))

rewrite51.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`times-frac_binary64`
77×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64`
65×	`add-cube-cbrt_binary64`
59×	`sqrt-prod_binary64`

Counts

4 → 169

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (/.f64 1 (/.f64 (PI.f64) 4))) (.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (/.f64 4 (PI.f64)))))
8.0ms	(.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))) (sqrt.f64 (/.f64 4 (PI.f64))))
5.0ms	(*.f64 f (/.f64 (PI.f64) 4))
3.0ms	(/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4))))

simplify268.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-def_binary64`
334×	`distribute-rgt-in_binary64`
309×	`associate-r_binary64`
291×	`associate-l_binary64`
243×	`cancel-sign-sub-inv_binary64`

Counts

217 → 277

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	360	8275
1	795	7265
2	2544	7174
3	4467	7174
4	4994	7174
5	4922	7174

prune1.3s (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	318	4	322
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	323	9	332

Error

1.3b

Counts

332 → 9

Alt Table

Status	Error	Program
	2.6b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (/.f64 (PI.f64) 4))) (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (sqrt.f64 (/.f64 4 (PI.f64))))))
	8.1b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (/.f64 (PI.f64) 4))) (log.f64 (pow.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))) (sqrt.f64 (/.f64 4 (PI.f64)))))))
	2.0b	(neg.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))) 3)))
	2.9b	(neg.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 (/.f64 (PI.f64) 4))) (log.f64 (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) (sinh.f64 (.f64 (/.f64 (PI.f64) 4) f)))))))))
	1.8b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (/.f64 (PI.f64) 4))) (.f64 (log.f64 (.f64 (sqrt.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4)))) (/.f64 (sqrt.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4)))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 (/.f64 4 (PI.f64))))))
	2.6b	(neg.f64 (fma.f64 4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)) (.f64 1/12 (.f64 f (*.f64 f (PI.f64))))))
✓	1.8b	(neg.f64 (+.f64 (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) 2))) (.f64 (/.f64 4 (PI.f64)) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4))))))))
	2.0b	(neg.f64 (.f64 (.f64 (sqrt.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 (/.f64 4 (PI.f64)))) (.f64 (sqrt.f64 (log.f64 (/.f64 (cosh.f64 (.f64 f (/.f64 (PI.f64) 4))) (sinh.f64 (*.f64 f (/.f64 (PI.f64) 4)))))) (sqrt.f64 (/.f64 4 (PI.f64))))))
	1.8b	(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))) 2) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (/.f64 (sqrt.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 f (/.f64 (PI.f64) 4))) (exp.f64 (neg.f64 (.f64 f (/.f64 (PI.f64) 4))))))) (sinh.f64 (.f64 f (/.f64 (PI.f64) 4)))))))))

Compiler

Compiled 12051 to 9220 computations (23.5% saved)

regimes6.0s (19.4%)

Accuracy

Total 0.4b remaining (21.6%)

Threshold costs 0.4b (21.6%)

Counts

565 → 1

Compiler

Compiled 141836 to 113826 computations (19.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	80
1	38	80
2	56	80
3	65	80
4	70	80
5	71	80
6	69	80

end323.0ms (1%)

Compiler: Compiled 440 to 349 computations (20.7% saved)

Details

analyze1.4s (4.5%)

sample12.1s (39%)

simplify48.0ms (0.2%)

prune4.0ms (0%)

localize13.0ms (0%)

series738.0ms (2.4%)

rewrite46.0ms (0.1%)

simplify357.0ms (1.2%)

prune523.0ms (1.7%)

localize17.0ms (0.1%)

series1.6s (5%)

rewrite109.0ms (0.4%)

simplify374.0ms (1.2%)

prune897.0ms (2.9%)

localize20.0ms (0.1%)

series2.1s (6.9%)

rewrite69.0ms (0.2%)

simplify364.0ms (1.2%)

prune688.0ms (2.2%)

localize16.0ms (0.1%)

series1.6s (5.1%)

rewrite51.0ms (0.2%)

simplify268.0ms (0.9%)

prune1.3s (4.1%)

regimes6.0s (19.4%)

simplify5.0ms (0%)

end323.0ms (1%)

Profiling